# How to prove that (tan b / tab a) > (b/a) whenever 0 < a < b < π/2?

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I am able to show that tan x > x for 0 < x < π/2 but this doesn't seems to get me through to the final conclusion I'm looking for.

I am able to show that tan x > x for 0 < x < π/2 but this doesn't seems to get me through to the final conclusion I'm looking for.

##### 1 Answer

Aug 7, 2017

Consider the function:

we have that:

Now, as

and

so that the function is strictly increasing and:

As for